A212352 Row sums of A047997.

0, 1, 3, 9, 25, 75, 235, 759, 2521, 8555, 29503, 103129, 364547, 1300819, 4679471, 16952161, 61790441, 226451035, 833918839, 3084255127, 11451630043, 42669225171, 159497648599, 597950875255, 2247724108771, 8470205600639

Offset

0,3

Comments

Also the number of nonempty subsets of {1..2n} with mean n, even bisection of A362046. - Gus Wiseman, Apr 15 2023

Links

Table of n, a(n) for n=0..25.

Formula

From Gus Wiseman, Apr 15 2023: (Start)

a(n) = A000980(n)/2 - 1.

a(n) = A047653(n) - 1.

a(n) = A133406(2n+1) - 1.

a(n) = A362046(2n).

(End)

Example

From Gus Wiseman, Apr 15 2023: (Start)
The a(1) = 1 through a(3) = 9 subsets:
  {1}  {2}      {3}
       {1,3}    {1,5}
       {1,2,3}  {2,4}
                {1,2,6}
                {1,3,5}
                {2,3,4}
                {1,2,3,6}
                {1,2,4,5}
                {1,2,3,4,5}
(End)

Mathematica

Table[Length[Select[Subsets[Range[2n]], Mean[#]==n&]], {n, 0, 6}] (* Gus Wiseman, Apr 15 2023 *)

Crossrefs

Equals A047653(n) - 1.

Row sums of A047997.

For median instead of mean we have A079309, bisection of A361801.

Even bisection of A362046, zero-based version A070925.

A000980 counts nonempty subsets of {1..2n-1} with mean n.

A007318 counts subsets by length.

A327475 counts subsets with integer mean.

A327481 counts subsets by mean.

Cf. A000975, A013580, A024718, A057552, A133406, A361866.

Sequence in context: A132835 A191354 A001189 * A198180 A101786 A354647

Adjacent sequences: A212349 A212350 A212351 * A212353 A212354 A212355

Keyword

nonn

Author

N. J. A. Sloane, May 16 2012

Status

approved